Shown in FIG. 1 is a prior art operational amplifier. Systematic offset voltage results when there is a mismatch (.DELTA.I) between the currents flowing in the collectors of the two input transistors, Q.sub.1 and Q.sub.2 (differential pair). The difference between these currents is divided by the transconductance (g.sub.m) of the input stage and the result is the systematic input offset voltage.
V.sub.IO =.DELTA.I/g.sub.m PA1 I.sub.C1 =I.sub.C6 -I.sub.C8 I.sub.C2 =I.sub.C9 -I.sub.C11 (Where I.sub.CN is the collector current of transistor Q.sub.N) PA1 I.sub.C6 =I.sub.C9 =I.sub.C1 +I.sub.C8 =I.sub.C2 +I.sub.C11 PA1 .DELTA.I=I.sub.C1 -I.sub.C2 =I.sub.C11 -I.sub.C8
The majority of the mismatch between the collector currents of transistors Q.sub.1 and Q.sub.2 is due to the mismatch in transistors Q.sub.18 and Q.sub.20. Since the bases of transistors Q.sub.18 and Q.sub.20 are connected to the same node, any difference in the magnitudes of their base currents results in an error current which flows into that node at the collectors of transistors Q.sub.11 and Q.sub.15. This error current causes a mismatch between the collector currents of transistors Q.sub.11 and Q.sub.15. The current mirror 20 composed of transistors Q.sub.12, Q.sub.13, Q.sub.15, and Q.sub.16 causes the collector currents of transistors Q.sub.15 and Q.sub.8 to be equal. The collector currents of transistors Q.sub.1 and Q.sub.2 are related to those of transistors Q.sub.8 and Q.sub.11 as follows:
Since I.sub.C6 and I.sub.C9 are equal (due to the biasing circuit),
Therefore, any mismatch in the base currents of transistors Q.sub.18 and Q.sub.20 translates into input collector current mismatch and thus input offset voltage.
There are at least two reasons that the base currents in transistors Q.sub.18 and Q.sub.20 might not be equal. Since the transistors are different types (NPN and PNP), their .beta.'s (ratio of collector to base current) will probably be different. Even if the bias currents provided by transistors Q.sub.19 and Q.sub.21 to Q.sub.18 and Q.sub.20, respectively, are equal, the base currents, I.sub.B18 and I.sub.B20, will be different if the .beta.'s are different. Thus the base currents will be mismatched unless the .beta.'s are mismatched by exactly the opposite ratio of the bias current mismatch (which is highly unlikely, and will change with temperature).